Question

The price of a certain property increased by 10% in the first year, decreased by 20% in the second year, and increased by 25% in the third year. What was the amount of the dollar decrease in the property price during the second year?(1) The price of the property at the end of the third year was $22,000.(2) The decrease in the property price over the first two years was $2,000 less than the increase in the property price during the third year.

Answer 1

1) $4400

2) $4400

Explanation:

Let

X = price in first year

Y = price in 2nd year

Z = price in 3rd year

A = price in the end of 3rd year

Y = 1.1 X

Z = 0.8 Y

substitute Y into Z get Z = 0.88 X

A = 1.25 Z= 1.25(0.88X) = 1.1 X

1)

(125/100) Z = 22000

Z = 22000 x 100 / 125 = 17600

Z = 0.8Y

Y = Z/0.8 = 1.25Z

Amount of dollar decrease in 2nd year = Y - Z

= 1.25Z - Z = 0.25Z = 0.25 x 17600 = 4400 dollar

2)

Decrease in price over first 2 years = Increase in property in 3rd year - 2000

Hence, X - Z = (A-Z) - 2000

X - 0.8X = 1.1 X - 0.88 X - 2000

X - 0.88X - 1.1X + 088X = -2000

-0.1 X = -2000

0.1 X = 2000

X = 20000

Amount of dollar decrease during 2nd year = Y - Z = 1.1X - 0.88X = 0.22X

= (0.22) x (20000) = 4400 dollars